Working directly with high-dimensional data—such as large tables of numbers or detailed sensor readings—can be inefficient and challenging. Instead, you can represent each data point with a much smaller set of numbers that capture only its most important features. This set of numbers forms a latent space: a compressed, abstract representation of the original data.

Think of your data as a collection of points scattered throughout a complex, high-dimensional space. An encoder function acts like a funnel, transforming these points into a much smaller, simpler latent space. Each point in the latent space preserves the essential information needed for analysis or generation.

In this latent space, similar data points are located close together, while different points are farther apart. This structure makes it easier for machine learning models to process, compare, and generate new data that shares the key characteristics of the original set.

Mathematically, you can describe the process of mapping data into a latent space using an encoder function. Given an input $x$, the encoder transforms it into a latent variable $z$:

Here, $x$ is your original data (such as an image), and $z$ is the latent code — a lower-dimensional, abstract representation that retains the most important features of $x$. The goal of representation learning is to discover such mappings that make downstream tasks (like classification, clustering, or generation) more effective and efficient.